Conventionally, there is well-known a hybrid vehicle including an engine and a motor generator capable of outputting power for driving respectively, which starts the engine and prohibits a driving under an engine stop condition when a vehicle speed exceeds a vehicle speed threshold value indicating a boundary of a region prohibiting an operation of the engine (for example, refer to Patent Document 1). In the hybrid vehicle, the vehicle speed threshold value indicating the boundary of the region prohibiting the operation of the engine is changed in accordance with a battery condition based on a battery temperature. Also, there is well-known a hybrid vehicle including an engine and a motor generator capable of outputting power for driving respectively, which drives with power only from the motor generator while stopping an operation of the engine when a vehicle speed is equal to or less than a predetermined motor drive enabling vehicle speed (for example, refer to Patent Document 2). In the hybrid vehicle, the motor drive enabling vehicle speed is controlled to be raised when a remaining capacity of a battery capable of supplying electric power to the motor generator is equal to or more than a predetermined value. In these hybrid vehicles, when the battery is in good condition or the remaining capacity of the battery is ensured, the operation stop of the engine is allowed in accordance with the vehicle speed, so that a deterioration of a drivability such as a reduction of an acceleration response due to a shortage of electric power upon starting engine under a high speed driving may slightly occur, however, fuel consumption of the engine is improve.    [Patent Document 1] Japanese Patent Laid-Open No. 2006-170128    [Patent Document 2] Japanese Patent Laid-Open No. 2004-023959